If OP is in southern Calif, there are 2 vines that came to my mind. At first, I thought it looked like Trachelospermum jasminoides (Star Jasmine), but I went out & looked at mine & there is no terminal leaf. So not that one. The other, Pandorea jasminoides, as Alison suggested, does have the terminal leaf & it is 2-pinnate (compound?), as Saltcedar asked about. Let's see if the pic I just took came out well enough to see. Each leaflet has 2 to 3 pairs & one terminal leaf. Hard to say, but it seems that way in Tskn's photo. Tskn can compare to theirs.

There are several milkweed vines, but the one I have is Cynanchum laeve/honeyvine. I can only tell you about my experiences with it. I don't get many visits from monarchs, so as a result, don't get many monarch eggs/cats on any milkweed. One year, a female laid many eggs on my honeyvine, and I reared the cats on it, because the other milkweed was all gone. It was good that the vine is aggressive and grows rapidly, because the cats ate SO many leaves, it took all of them. Honeyvine doesn't have the "milk" that other MWs do, so maybe that's why it took so many of them? I don't know, but all the cats lived and emerged as perfect adults. I think I've got a picture of two of them, I'll check. The vine itself is somewhat invasive here, but I just pull it up where I don't want it. It is NOT poisonous to monarchs - I don't know where this internet source is, but a lot of people must be reading and believing it, because they ask about it a lot. I personally love it, because I have trouble growing other milkweeds - only swamp MW/A. incarnata and tropical MW/A. curassavica are easy for me to grow. Here's the picture - As a bonus, honeyvine flowers attract a lot of interesting bugs and butterflies. They smell strongly of coconut oil, and hairstreaks especially show up on them. Sherry

That might depend on where you live in Houston. I used to live in the Tomball/Spring area, and you would think, that being farther North, it would be cooler than here in Pasadena. But Pasadena gets a lot of cool air from the ocean, so its actually easier to grow plants here, because there is more shade, since neighborhoods have established trees, and because the heat doesn't wilt my plants as much. I haven't seen a lot of Bougainvillea growing in north houston, but I see it all over south of downtown. And it seems to do really well- the bushes/trellies of bougainvillea here look very healthy and full. However, maybe its my soil, but my rose bush, a teacup hybrid, is doing very well, even though its not in the sun quite as much as recommended. (Oddly enough, though my first blossom was dark red, now all the flowers coming in are a hot pink.) So what I would do is think about how much shelter your plants will be getting- bougainvillea does much better with the scorching heat, but roses in the area seem to do a bit better during hurricane season- and how fast the plant will spread. Do you mind that it might be a couple years before your roses climb to the top of your trellis?

Can you take a photo of the stem twining around the tree? Often having a closeup along with a photo that shows a larger part or all of a plant helps. In this case the way oriental bittersweet twines is fairly distinctive.